Algorithms for Generating Maximin Latin Hypercube and Orthogonal Designs

Moon, Hyejung; Dean, Angela; Santner, Thomas J.

doi:10.1080/15598608.2011.10412052

Cited by 40 publications

(23 citation statements)

References 14 publications

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“…To address this, a number of researchers have developed algorithms to reduce or eliminate correlations among columns of a Latin hypercube and improve on their space-filling properties (Florian, 1992;Owen, 1994;Ye, 1998;Steinberg and Lin, 2006;Cioppa and Lucas, 2007;Joseph and Hung, 2008;Pang et al, 2009;Sun et al, 2009;Moon et al, 2011;Vieira, et al, 2011;Hernandez et al, 2012;Vieira, et al, 2013;Yang et al, 2013). A Latin hypercube with no correlation between any of its input variables is an orthogonal Latin hypercube (OLH).…”

Section: Latin Hypercubes and Other Space-filling Designsmentioning

confidence: 99%

“…In addition, they used a weighted average of a distance metric and the average column correlation among the main effect terms as their fitness function. Moon et al (2011) developed algorithms for generating maximin Latin hypercube and orthogonal designs that show improvements to the existing algorithms under a variety of criteria. These aforementioned algorithms construct designs that optimize a number of different criteria.…”

Section: Introductionmentioning

confidence: 99%

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Second-order nearly orthogonal Latin hypercubes for exploring stochastic simulations

MacCalman

Vieira

Lucas

2017

Journal of Simulation

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Naval Postgraduate School, Monterey, USA This paper presents new Latin hypercube designs with minimal correlations between all main, quadratic, and two-way interaction effects for a full second-order model. These new designs facilitate exploratory analysis of stochastic simulation models in which there is considerable a priori uncertainty about the forms of the responses. We focus on understanding the underlying complexities of simulated systems by exploring the input variables' effects on the behavior of simulation responses. These new designs allow us to determine the driving factors, detect interactions between input variables, identify points of diminishing or increasing rates of return, and find thresholds or change points in localized areas. Our proposed designs enable analysts to fit many diverse metamodels to multiple outputs with a single set of runs. Creating these designs is computationally intensive; therefore, several have been cataloged and made available online to experimenters.

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Section: Latin Hypercubes and Other Space-filling Designsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Second-order nearly orthogonal Latin hypercubes for exploring stochastic simulations

MacCalman

Vieira

Lucas

2017

Journal of Simulation

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“…In our examples, we use a criterion that maximizes the minimum interpoint distance within all twodimensional subspaces of the input space. Moon et al (2011) showed that not only does the construction of such designs save considerable computing time, but the designs tend to perform well also under a maximin criterion in the (n − 1)-dimensional space.…”

Section: Gsince Initialization Stagementioning

confidence: 99%

Two-Stage Sensitivity-Based Group Screening in Computer Experiments

2012

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Sophisticated computer codes that implement mathematical models of physical processes can involve large numbers of inputs, and screening to determine the most active inputs is critical for understanding the inputoutput relationship. This article presents a new two-stage group screening methodology for identifying active inputs. In Stage 1, groups of inputs showing low activity are screened out; in Stage 2, individual inputs from the active groups are identified. Inputs are evaluated through their estimated total (effect) sensitivity indices (TSIs), which are compared with a benchmark null TSI distribution created from added low noise inputs. Examples show that, compared with other procedures, the proposed method provides more consistent and accurate results for high-dimensional screening. Additional details and computer code are provided in supplementary materials available online.

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“…To achieve multi-dimensional space-filling property, various optimality criteria have been proposed. These include maximin distance criterion (Morris and Mitchell (1995)), multi-dimensional projection (Tang (1993); Moon, Dean, and Santner (2011)), orthogonality and near orthogonality (see, for example, Sun, Liu, and Lin (2009) ;Yang and Liu (2012); Georgiou and Efthimiou (2014)), and the discrepancy criterion (Fang et al (2000)). Attempts have also been made to seek designs based on multiple optimality criteria.…”

Section: Introductionmentioning

confidence: 99%

A general construction for space-filling Latin hypercubes

Lin¹,

Kang²

2017

STAT SINICA

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We propose a general method for constructing Latin hypercubes of flexible run sizes for computer experiments. The method makes use of arrays with a special structure and Latin hypercubes. By using different such arrays and Latin hypercubes, the proposed method produces various types of Latin hypercubes including orthogonal and nearly orthogonal Latin hypercubes, sliced Latin hypercubes, and Latin hypercubes in marginally coupled designs. In addition, the proposed algebraic design construction is particularly efficient as it does not need any optimization search but still produces Latin hypercubes whose space-filling properties are comparable with those generated by the common and latest methods in the literature.

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Algorithms for Generating Maximin Latin Hypercube and Orthogonal Designs

Cited by 40 publications

References 14 publications

Second-order nearly orthogonal Latin hypercubes for exploring stochastic simulations

Second-order nearly orthogonal Latin hypercubes for exploring stochastic simulations

Two-Stage Sensitivity-Based Group Screening in Computer Experiments

A general construction for space-filling Latin hypercubes

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